Enigma 1199: An Enigma’s meaning

In the numbers ENIGMA, MEANING and IDEA digits have been consistently replaced by letters, with different letters used for different digits. I have tested the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 to see if they are a common factor of both ENIGMA and MEANING.

Of course 1 is a common factor of them, and it turns out that nine of the numbers 1-12 are common factors of ENIGMA and MEANING (and indeed the other three numbers are factors of IDEA).

The three numbers not common factors of ENIGMA and MEANING are either
a) 5,7,10, so 70 doesn’t divide ENIGMA and MEANING but does divide IDEA
or
b) 5,10,11 so 110 doesn’t divide ENIGMA and MEANING but does divide IDEA